I certainly sympathise, but the twins in the twin paradox are not equivalent, whatever inertial frame you use to observe them. This is because the one that jets off in the rocket, and eventually returns to the earth has undergone a lot of acceleration, which his brother hasn't.

Right, the specific case (the usual textbook version of the 'twin paradox' - but not actually the

*paradoxical* version) with one traveller and one stay-at-home, where both agree that only the traveller was accelerated, is that second kind of time dilation I mentioned: 'non-observer-dependent round-trip dilation of an objectively accelerated vs less-unaccelerated observer'.

A clearer version of the twins paradox - the one where there's an actual paradox - is: what happens if

*both* twins take identical but opposite journeys away from the Earth?

By the 'spacetime interpretation' of relativity, the answer is, on its surface, simple and non-paradoxical, and it's what you'll find in the textbooks: neither twin in this case ages slower than the other, they both return to Earth at the same moment and are the same age. But they do both age slower than the Earth because they were more accelerated (relative to a shared inertial reference frame common to both twins and the Earth), therefore they took shorter journeys in spacetime.

So far so good. But on both the inbound and the outbound journeys, when they're not speeding up or slowing down, each twin is moving at a high velocity relative to the other. According to the simple observer-dependent SR time dilation for straight-line unaccelerated relative motion, each twin should be seriously time dilated at this point. However SR is reciprocal, so it allows each twin to consider the other twin aging faster than itself at all points other than the actual acceleration (and also during the acceleration). So at the end of the journey, why don't all those time dilations add up? Presumably we can't just use a simple addition formula, but the exact transformation must be quite complicated, and must shove a huge amount of time-change into that short period of acceleration.

So a naive application of Special Relativity gives us three answers for time dilation: 1. Twin A thinks it ages slower than twin B, because it measures B moving relatively to itself. 2. Twin B thinks it ages faster than A, because it measures A moving relatively to itself. 3. Neither twin actually ages faster than the other, because they both took 'equivalent paths in spacetime', ie, they were accelerated relatively to a shared inertial frame (the Earth). 4. From Earth's perspective, using the naive SR calculation, both twins also age faster than it, but this is purely because of their observed high relative velocities - it's only an accident of the maths that Earth can consider itself 'less accelerated' than the twins, because it doesn't know how much 'actual' or 'felt' acceleration the twins are really undergoing.

(In fact, in any real Twin situation, Earth must also be getting some acceleration / taking a shorter path in spacetime because of gravity (both the Sun's or its own). But if we have to feel an acceleration to do relativity correctly, ie to know if we're in an accelerated or inertial frame, how do we calculate gravitational time dilation accurately when we can't feel its acceleration?)

It seems that 1 and 2 must be illusions (or at least observations of emitted light or radio pulses) and only 3 and 4 are 'real'. But 1 and 2 AND 4 come straight from the basic SR equation - the Lorentz transform. It seems very odd that a theory gives you two wrong or illusory answers in the simplest case (straight-line relative motion), only gives you the correct answer after you look at a much more complex case (closed-loop curved motion, where you take into account not just the observed relative motions and the relative accelerations, but the

*felt* acceleration of each observer, and keep track of the whole flight history. Shouldn't a consistent theory build the complex case out of the simple cases, not the other way around? If you take just one observation while you're in straight-line flight, and you don't know whether you previously accelerated or not, can you calculate your time dilation accurately?

Relativity is theoretically based on relative motion. But it seems when you actually use it in practice (for closed-loop paths) you

*can't *just use relative motion but have to bring in the idea of 'felt' or 'absolute' acceleration.

It also seems odd that a theory of space and time would require space and time to shift based on velocity, which is a ratio of space and time. Isn't that something of a circular definition? Presumably we can escape from the circular definition by saying each observer is changing (their idea of)

*another *observer's space and time, not their own, but... that's when my head starts to hurt. In our everyday world, we assume as a matter of course that space and time exist for all observers; that if A measures a distance X to B, then B will measure distance X to A; and each will measure their relative velocity based on (measured) X. But if you're changing the units of measured space and time

*based on a function of those units themselves*, none of this becomes obvious or trivial.

It also seems that you have to bring in a concept of 'shifting of the planes of simultaneity' when you accelerate; such that you change your beliefs about the time and distance of all other objects. But presumably those distant objects didn't actually change their position in 'space and time' based on your local movements; so that the 'space and time' which you believe changed due to your acceleration must actually really only exist in your mind.

So there seem to be two separate, unrelated yet freely interchanged concepts of space and time in relativity: 'real' or 'physical' space/time, modelled by the GR tensor, agreed on by all observers when they return after round-trips, and 'imaginary' or 'observed' space and time which is really just numbers calculated from light signals, modelled by the SR Lorentz Transform, which only exists in an observers mind, and on which observers disagree. But both concepts seem to use the same sets of coordinates and the same equations.

Also, the entire idea of the distance and time of a distant event being a function of a velocity comparison with a potentially infinite number of distant observers seems to become more odd the more I think about it: because relativity is, above all, a local theory, not wanting to bring in a concept of instant-action-at-a-distance. Yet 'the relative velocity of two distant objects' is not in the least a local concept. Two distant objects have no means of directly measuring their relative velocity! Wouldn't a truly local theory be one that had an aether, so that the velocity state of all particles would simply be their velocity relative to the

*local aether*? Einstein wanted to remove any idea of an aether because it was in principle unmeasurable, but taking it away just seems to lead to endless spiralling complexities. At some point, shouldn't simplicity of computation justify allowing one not-directly-measurable quantity?

It all feels as if someone tried to remove the concept of 'zero' from arithmetic, on the grounds that it stood for nothing and could not be measured and therefore should not be part of the system, and then tried to make it consistent.

No doubt an actual relativity expert would be beating their head here to say that I have everything completely wrong and am just confusing everybody, and I probably do and am. But this is the kind of confusion I get when I try to think seriously about what SR implies. And Dingle's questions went along a very similar line (and got a similar response from the experts; baffled incomprehension on both sides).

Regards, Nate